1. In a covered saucepan, poach chicken in broth over medium-low heat until white throughout, 12 to 15 minutes. Remove chicken with a slotted spoon and bring broth to a boil. Add rice; reduce heat to low, and cover pan. Simmer until all of liquid is absorbed and rice is tender, about 18 minutes. When chicken is cool enough to handle, cut into thin strips.
2. In a small bowl, whisk together olive oil, vinegar, mustard, cumin, salt, and pepper. Stir in tomatoes, bell pepper, red onion, and jalapeno pepper. In a large bowl, combine about two-thirds of vinaigrette with warm rice. Toss to mix.
3. To serve, spoon rice onto a bed of lettuce leaves. Arrange chicken strips on top. Spoon remaining vinaigrette over salad. Serve garnished with cilantro.